## Boundaries of a Model

Now that we have fully assigned material to the entire grid, the external boundaries of the water need to be set up correctly to reflect how the areas beyond the model would behave in the real world. OnScale has a number of pre-defined boundary conditions to be applied by the user with the boun side command. The most commonly used boundary conditions are:

• free
• nodes can move freely with no external forces acting upon them
• When to use: edge of model is at
• symm
• boundary for symmetrical geomtries
• assumed that what occurs on one side occurs on the other
• When to use: model is the same geometrically and electrically across the boundary
• absr
• energy continues past boundary with no reflections
• When to use: edge of model continues infinitely with the same material (typically a large body of water)
• fixd
• nodes are completely fixed - zero displacement
• energy is perfectly reflected
• When to use: edge of model is infinitely stiff

The model should be set up with the following boundaries to simulate the PZT disc in a infinite body of water:

c external boundary conditions
boun
side xmin symm    /* assign symmetry condition xmin side of model
side xmax absr    /* assign absorbing boundary condition (infinite medium)
side ymin absr    /* to xmax ymin and ymax side
side ymax absr
end

## Time Functions & Piezoelectric Loads

The model has now been fully geometrically defined which means we can technically execute the model however, the model will remain static over time. We need to provide some form of input to stimulate the model which typically falls into 2 categories:

1. Pressure loads - for simulating purely mechanical wave problems
2. Piezoelectric loads - for simulating piezoelectric devices

Before we set up the loading conditions, an input waveform, also referred to as a Time Function, is required. OnScale provides a variety of Time Functions to use in the model ranging from sinusoids, wavelets and user-defined functions too. See func for a full list of input types. There is also a Time Function Tool to set up and visualise the input signals to be used within the model.

Tip: OnScale recommends using the Ricker Wavelet (wvlt) time function due to its broadband performance and low spectral leakage beyond 2.5x the centre frequency.

c define time varying function
func wvlt \$freqint 1.	/* wavelet impulse function

symb ascale = 1	/* area scaling for electrode area - required for accurate simulation of impedance amplitude - '1' for axiy model

piez
wndo \$i1 \$i2 \$j2 \$j3    /* define electric window to pzt material - minimise for faster model run time

defn top \$ascale        /* define electrode - name 'top'
node \$i1 \$i2 \$j3 \$j3    /* assign nodes for top electrode

defn bot \$ascale        /* define electrode - name 'bot'
node \$i1 \$i2 \$j2 \$j2    /* assign nodes for bottom electrode

/* electrical boundary condition
bc top volt func    /* apply voltage condition to 'top' electrode and assign driving signal 'func'
bc bot grnd         /* apply ground condition to 'bot' electrode

slvr pard    /* use pardiso solver - our new faster electrostatic solver for piezo simulations
end

Defining the piezoelectric load requires the piez primary command and the following subcommands:

• wndo
• Define the electric window - the region of the grid desginated for the electro-mechanical calculation
• OnScale uses a hybrid method for the calculation by using an implicit (for the electrical calculations)and explicit solver (for the mechanical calculations) to minimise runtime.

Tip: Always try to minimise the electric window size to reduce model runtime and memory requirements.

• defn
• To initiate the definition of an electrode within the model with a reference name
• Also used to set the electrode area scaling to accurately simulate the capacitance of a piezoelectric device
• The simulated area must be same as the electrode area on your physical device
• For 2D models - must multiply by the dimension in the unmodelled direction and account for any symmetry conditions (x2 multiplier for each symm condition)
• For 2D axisymmetric models - no scaling is required as solver knows the exact size of device
• For 3D models - only need to account for symmetry conditions(x2 multiplier for each symm condition)
• node
• define the exact nodes on the grid to create the electrical boundary
• node command must follow the defn command
• bc
• applies electrical boundary conditions (ground, voltage, open etc...) to the electrodes generated by the defn and nodecommands
• slvr
• Selects the solver to use for the electrostatic calculations.
• pard is typically the fastest solver especially for large piezoelectric models

Tip: Alternative solvers will be slower however, some will offer a solution using much less memory if there are hardware limitations. See slvr.

Within the PZT2D.flxinp file:

1. Using the boun primary command apply symmetry (symm) to xmin side and absorbing (absr) boundaries to the xmax, ymin and ymax sides using the side subcommand.
2. Using the func primary command set up the Ricker Wavelet with the wvlt subcommand - set the the frequency argument to \$freqint and the peak voltage amplitude to 1V
3. Create a symbol variable called ascale and set it to a value of 1 - (used for electrode area scaling)
4. Using the piez primary command:
1. Use the wndo set up the electric window region around the PZT material (i1 to i2 & j2 to j3)
2. Use the defn subcommand to create an electrode called top and apply the \$ascale variable for the area scaling
3. Use the node subcommand to assign the nodes on the top surface of the PZT to top (i1 to i2 & j3 to j3)
4. Use the defn subcommand to create an electrode called bot and apply the \$ascale variable for the area scaling
5. Use the node subcommand to assign the nodes on the bottom surface of the PZT to bot (i1 to i2 & j2 to j2)
6. Use the bc subcommand to set the top electrode with a voltage (volt) type boundary condition and apply the time function (func) as the electrical condition
7. Use the bc subcommand to set the bot electrode with grounded (grnd) electrical condition
8. Use the slvr subcommand to set the electrostatic solver to the PARDISO (pard) solver

Progress to tutorial section: Model Outputs

## Tutorial Code

c external boundary conditions
boun
side xmin symm    /* assign symmetry condition xmin side of model
side xmax absr    /* assign absorbing boundary condition (infinite medium)
side ymin absr    /* to xmax ymin and ymax side
side ymax absr
end
c define time varying function func wvlt \$freqint 1. /* wavelet impulse function c piezoelectric loads symb ascale = 1 /* area scaling for electrode area - required for accurate simulation of impedance amplitude - '1' for axiy model piez wndo \$i1 \$i2 \$j2 \$j3 /* define electric window to pzt material - minimise for faster model run time defn top \$ascale /* define electrode - name 'top' node \$i1 \$i2 \$j3 \$j3 /* assign nodes for top electrode defn bot \$ascale /* define electrode - name 'bot' node \$i1 \$i2 \$j2 \$j2 /* assign nodes for bottom electrode /* electrical boundary condition bc top volt func /* apply voltage condition to 'top' electrode and assign driving signal 'func' bc bot grnd /* apply ground condition to 'bot' electrode slvr pard /* use pardiso solver - our new faster electrostatic solver for piezo simulations end
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